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“Backward Differential Flow” May Not Converge to a Global Minimizer of Polynomials

Author

Listed:
  • Orhan Arıkan

    (Bilkent University)

  • Regina S. Burachik

    (University of South Australia)

  • C. Yalçın Kaya

    (University of South Australia)

Abstract

We provide a simple counter-example to prove and illustrate that the backward differential flow approach, proposed by Zhu, Zhao and Liu for finding a global minimizer of coercive even-degree polynomials, can converge to a local minimizer rather than a global minimizer. We provide additional counter-examples to stress that convergence to a local minimum via the backward differential flow method is not a rare occurence.

Suggested Citation

  • Orhan Arıkan & Regina S. Burachik & C. Yalçın Kaya, 2015. "“Backward Differential Flow” May Not Converge to a Global Minimizer of Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 401-408, October.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:1:d:10.1007_s10957-015-0727-7
    DOI: 10.1007/s10957-015-0727-7
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    Cited by:

    1. Orhan Arıkan & Regina S. Burachik & C. Yalçın Kaya, 2020. "Steklov regularization and trajectory methods for univariate global optimization," Journal of Global Optimization, Springer, vol. 76(1), pages 91-120, January.

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